Finite Group DatabasebetaFinite Group Databasebeta| order | 2176 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#2201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C17 |
| prime radical | C17×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C17 ◁ C2×D4×C17 ◁ G | |
226 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,25)(22,26)(23,27)(24,30)(29,45)(31,44)(32,43)(33,39)(34,40)(35,42)(36,46)(37,47)(38,48)(41,49);(18,20,23,31)(19,24,27,37)(21,32,34,29)(22,30,35,47)(25,38,40,36)(26,28,42,44)(33,48,49,46)(39,43,41,45);(18,21,23,34)(19,25,27,40)(20,29,31,32)(22,33,35,49)(24,36,37,38)(26,41,42,39)(28,43,44,45)(30,46,47,48)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2176, 933);